Degree and Radian Measure Formula

Degree and Radian Measure Formula

In mathematics, the radian is the standard unit of angular measure. An angle’s measurement in radians is numerically equal to the length of a corresponding arc of a unit circle. The relationship or the connection between the arc length and radius of a circle defines the radian of a circle. Degree and radian formula used to convert, degree to radian or radian to degree.

\[\LARGE Radian=\frac{Arc\;Length}{Radius\;Length}\]

\[\LARGE Radian=\frac{Degree\times \pi}{180}\]

Here are few Degree Measures and their corresponding Radian Measures – 

30° = π/6

45° = π/4

60° = π/3

90° = π/2

120° = 2π/3

135° = 3π/4

150° = 5π/6

180° = π

210° = 7π/6

225° = 5π/5

240° = 4π/3

270° = 3π/2

300° = 5π/3

315° = 7π/4

330° = 11π/6

360° = 2π

Solved Example

Question:

Convert 220° into radian measure.

Solution:

Given,

Degree = 220°

We know that,

Radian =  

\(\begin{array}{l}\frac{degree \times \pi}{180}\end{array} \)

Radian =

\(\begin{array}{l}\frac{220 \times \pi}{180}\end{array} \)

Radian =

\(\begin{array}{l}\frac{11 \times \pi}{9}\end{array} \)

Radian =

\(\begin{array}{l}0.837\end{array} \)

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